The maximum value of z = 9x + 13y subject to 2x + 3y le 18, 2x + y le 10, x ge 0, y ge 0 is

Question

The maximum value of z = 9x + 13y subject to 2x + 3y le 18, 2x + y le 10, x ge 0, y ge 0 is (A)  130  (B)  81  (C)  79  (D)  99

Tardigrade Admin · Accepted Answer

The feasible region is OABC. <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/87f53cd52619d12d2796670347721ee6-.png" /> At O(0,0), z=0 At A(5,0), z=45 At B(3,4), z=27+52=79 At C(0,6), z=78 ∴ Maximum value of z is 79

Q. The maximum value of $z = 9 x + 13 y$ subject to $2 x + 3 y \leq 18, 2 x + y \leq 10, x \geq 0, y \geq 0$ is

$130$

$81$

$79$

$99$

The feasible region is $O A BC$ .

At $O (0, 0), z = 0$
At $A (5, 0), z = 45$
At $B (3, 4), z = 27 + 52 = 79$
At $C (0, 6), z = 78$
$∴$ Maximum value of $z$ is $79$

Q. The maximum value of z=9x+13y subject to 2x+3y≤18,2x+y≤10,x≥0,y≥0 is

130

81

79

99